The time evolution of the plasma distribution functions (electrons and ions
) in dusty plasmas is found solving numerically the equations of the kineti
c theory of dusty plasmas [Tsytovich and de Angelis, Phys. Plasmas 6, 1093
(1999); 7, 554 (2000)]. The role and importance of the plasma source and pa
rticle diffusion are investigated. The "equilibrium" distributions (asympto
tic solutions) are used to calculate the static screening of a dust particl
e, and the difference with the usual result (Debye screening) of a three-co
mponent plasma is shown for various parameter regimes. (C) 2001 American In
stitute of Physics.